In a large saucepan, melt the butter over medium heat. Once melted, stir in the corn syrup, vanilla extract, and a pinch of salt. Mix well until combined.
Add the mini marshmallows to the saucepan and stir continuously until they are completely melted and smooth.
Remove the saucepan from heat and gently fold in the Golden Grahams cereal until evenly coated with the marshmallow mixture.
Line a 9x9-inch baking dish with parchment paper, leaving some overhang for easy removal. Pour the cereal mixture into the dish and press it down firmly with a spatula to create an even layer.
Sprinkle the milk chocolate chips evenly over the top of the pressed cereal mixture. Allow the chocolate to soften for a few minutes, then use a spatula to spread it evenly over the surface.
Let the mixture cool at room temperature for about 30 minutes, or until set. Once set, lift the bars out of the baking dish using the parchment paper and cut into squares.